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A099448 A Chebyshev transform of A030191 associated to the knot 7_6. 1
1, 5, 19, 65, 216, 715, 2369, 7855, 26051, 86400, 286549, 950345, 3151831, 10453085, 34667784, 114976135, 381319781, 1264651795, 4194233399, 13910227200, 46133441401, 153002131805, 507433471819, 1682909416265, 5581389996216 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The denominator is a parameterization of the Alexander polynomial for the knot 7_6. The g.f. is the image of the g.f. of A030191 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
LINKS
Dror Bar-Natan, The Rolfsen Knot Table
FORMULA
G.f.: (1+x^2)/(1-5x+7x^2-5x^3+x^4); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(n-2k-j, j)(-5)^j*5^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A030191(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A030191(k)/2}; a(n)=sum{k=0..n, A099449(n-k)*binomial(1, k/2)(1+(-1)^k)/2};
MATHEMATICA
CoefficientList[Series[(1+x^2)/(1-5x+7x^2-5x^3+x^4), {x, 0, 30}], x] (* or *)
LinearRecurrence[{5, -7, 5, -1}, {1, 5, 19, 65}, 30] (* Harvey P. Dale, Nov 27 2013 *)
CROSSREFS
Sequence in context: A025568 A001047 A359919 * A239618 A124806 A059509
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 16 2004
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)